Communication efficient sparse-reduce in distributed machine learning

ABSTRACT

A method is provided for sparse communication in a parallel machine learning environment. The method includes determining a fixed communication cost for a sparse graph to be computed. The sparse graph is (i) determined from a communication graph that includes all the machines in a target cluster of the environment, and (ii) represents a communication network for the target cluster having (a) an overall spectral gap greater than or equal to a minimum threshold, and (b) certain information dispersal properties such that an intermediate output from a given node disperses to all other nodes of the sparse graph in lowest number of time steps given other possible node connections. The method further includes computing the sparse graph, based on the communication graph and the fixed communication cost. The method also includes initiating a propagation of the intermediate output in the parallel machine learning environment using a topology of the sparse graph.

RELATED APPLICATION INFORMATION

This application claims priority to provisional application Ser. No.62/506,660 filed on May 16, 2017, incorporated herein by reference. Thisapplication is a continuation-in-part of U.S. patent application Ser.No. 15/480,874, filed on Apr. 6, 2017, entitled “Fine-GrainSynchronization in Data-Parallel Jobs for Distributed Machine Learning”,incorporated herein by reference. This application is also related toanother continuation-in-part of U.S. patent application Ser. No.15/480,874, filed on Apr. 6, 2017, entitled “Fine-Grain Synchronizationin Data-Parallel Jobs for Distributed Machine Learning”, filedconcurrently herewith, incorporated herein by reference.

BACKGROUND Technical Field

The present invention relates to information processing, and moreparticularly to fine-grain synchronization in data-parallel jobs fordistributed machine learning.

Description of the Related Art

Big-data processing involves multiple parallel workers, or multipleworkers and a single master. Existing worker synchronization istypically performed using a barrier primitive or via a file-system(stage wise synchronization). Examples of big-data processing tasksinclude data parallel tasks such as large-scale machine learning andgraph analysis. Specific tasks with distributed machine learning includetraining data-parallel models for large-scale surveillance, languagetranslation, and image recognition.

In large-scale surveillance, large-scale surveillance models can becaptured on tens of thousands of training set videos. These videos canbe trained over data-parallel distributed machine learning systems. Eachnode in a distributed training replica processes a bunch of videos andupdates the training model. The nodes then coordinate and share theupdates periodically. Finally, this trained model is deployed invehicular systems or surveillance systems to run predictions.

In these parallel learning systems, models learn on new data usingalgorithms such as gradient descent to generate an update to the modelparameters. Individual models periodically transmit model updates in an“all-reduce” step. Model updates can be parameters or gradients. Herein,parameter updates and gradient updates can be collectively referred toas “model updates”. Moreover, the terms “machine” and “node” are usedinterchangeably herein. All-reduce is a parallel programming primitivein which an aggregate function (such as average) of locally computedmodels is computed and sent to all nodes. The models receive gradientsand average them with their own locally computed sub-gradients, on everyiteration (or every few iterations). However, if the network of nodes issparsely connected, the convergence may be slow due to stale updatesbeing passed around. However, there are savings in network and CPU costs(fewer updates), that may result in an overall speedup.

Barrier synchronization is an important and widely used operation forsynchronizing parallel systems. Upon encountering a barrier operation, aprocess waits until all processes in the system have reached a barrier.The barrier operation is the most commonly used synchronizationprimitive in data-parallel primitive.

However, this style of synchronization suffers from several problems.First, barrier primitives are slow and removing such a primitive(asynchronous) breaks down correctness semantics. Second, most barrierimplementations synchronize with all processes and may be slow tosynchronize a subset of workers. Third, using a barrier with thebulk-synchronous processing paradigm described suffers frommixed-version issues; that is, in absence of receive sidesynchronization, there may be torn-reads and over-writes. This isbecause a barrier gives no information if the recipient has seen orprocessed the gradient and additional expensive synchronization may berequired. Finally, using a barrier also causes network resource spikessince all workers will send intermediate values at the same time.

Additionally, adding extra barriers before/after push and reduce doesnot product a strongly consistent BSP that can incorporate model updatesfrom all replicates since the actual send operation may be synchronousand there is not guarantee that receives receive these messages whenthey perform a reduce. Unless a blocking receiver is added after everysend, the consistency is not guaranteed. However, this introduces asignificant synchronization overhead.

Thus, there is a need for improved synchronization in data paralleljobs, particularly involving large-scale surveillance.

SUMMARY

According to an aspect of the present invention, a computer-implementedmethod is provided for sparse communication in a parallel machinelearning environment. The method includes determining, by a processor, afixed communication cost for a sparse graph to be computed. The sparsegraph is (i) determined from a communication graph that includes all themachines in a target cluster of the parallel machine learningenvironment, and (ii) represents a communication network for the targetcluster having (a) an overall spectral gap greater than or equal to aminimum threshold, and (b) certain information dispersal properties suchthat an intermediate output from a given node disperses to all othernodes of the sparse graph in lowest number of time steps given otherpossible node connections. The method further includes computing, by theprocessor, the sparse graph, based on the communication graph and thefixed communication cost. The method also includes initiating, by theprocessor, a propagation of the intermediate output in the parallelmachine learning environment using a topology of the sparse graph.

According to another aspect of the present invention, a computer programproduct is provided for sparse communication in a parallel machinelearning environment. The computer program product includes anon-transitory computer readable storage medium having programinstructions embodied therewith. The program instructions are executableby a computer to cause the computer to perform a method. The methodincludes determining, by a processor of the computer, a fixedcommunication cost for a sparse graph to be computed. The sparse graphis (i) determined from a communication graph that includes all themachines in a target cluster of the parallel machine learningenvironment, and (ii) represents a communication network for the targetcluster having (a) an overall spectral gap greater than or equal to aminimum threshold, and (b) certain information dispersal properties suchthat an intermediate output from a given node disperses to all othernodes of the sparse graph in lowest number of time steps given otherpossible node connections. The method further includes computing, by theprocessor, the sparse graph, based on the communication graph and thefixed communication cost. The method also includes initiating, by theprocessor, a propagation of the intermediate output in the parallelmachine learning environment using a topology of the sparse graph.

According to yet another aspect of the present invention, a computerprocessing system is provided for sparse communication in a parallelmachine learning environment. The computer processing system includes amemory for storing program code. The computer processing system furtherincludes a processor for running the program code to determine a fixedcommunication cost for a sparse graph to be computed. The sparse graphis (i) determined from a communication graph that includes all themachines in a target cluster of the parallel machine learningenvironment, and (ii) represents a communication network for the targetcluster having (a) an overall spectral gap greater than or equal to aminimum threshold, and (b) certain information dispersal properties suchthat an intermediate output from a given node disperses to all othernodes of the sparse graph in lowest number of time steps given otherpossible node connections. The processor is further configured to runthe program code to compute the sparse graph, based on the communicationgraph and the fixed communication cost. The processor is also configuredto run the program code to initiate a propagation of the intermediateoutput in the parallel machine learning environment using a topology ofthe sparse graph.

These and other features and advantages will become apparent from thefollowing detailed description of illustrative embodiments thereof,which is to be read in connection with the accompanying drawings.

BRIEF DESCRIPTION OF DRAWINGS

The disclosure will provide details in the following description ofpreferred embodiments with reference to the following figures wherein:

FIG. 1 is a block diagram illustrating an exemplary processing system towhich the present principles may be applied, according to an embodimentof the present principles;

FIG. 2 shows an exemplary environment to which the present invention canbe applied, in accordance with an embodiment of the present principles;

FIG. 3 shows an exemplary synchronization condition to which the presentinvention can be applied, in accordance with an embodiment of thepresent principles;

FIG. 4 shows an exemplary synchronization condition, in accordance withan embodiment of the present principles;

FIG. 5 shows an exemplary method for fine-grain synchronization of dataparallel jobs, in accordance with an embodiment of the presentprinciples;

FIG. 6 shows another exemplary method for fine-grain synchronization ofdata parallel jobs, in accordance with an embodiment of the presentprinciples;

FIG. 7 shows a comparison involving an all-reduce and a parameter serverto which the present invention can be applied, and a spectral reduce inaccordance with an embodiment of the present invention;

FIG. 8 shows a method for communication efficient sparse-reduce in adistributed machine learning environment, in accordance with anembodiment of the present invention; and

FIG. 9 shows a method for measuring node diffusion efficiency, inaccordance with an embodiment of the present invention.

DETAILED DESCRIPTION OF PREFERRED EMBODIMENTS

In an embodiment, the present invention relates to fine-grainsynchronization in data-parallel jobs for distributed machine learning.

In another embodiment, the present invention relates to fine-grainedsynchronization for data-parallel tasks in a big data processingenvironment.

In yet another embodiment, the present invention relates tocommunication efficient sparse-reduce in distributed machine learning.This embodiment can involve providing a methodology to determine theunderlying sparse network

Hence, embodiments of the present invention will be initially describedwith respect to fine-grained synchronization in data parallel jobs in abig data processing environment. Thereafter, embodiments of the presentinvention will be described with respect to fine-grained synchronizationin data parallel jobs for distributed machine learning. Thereafterstill, embodiments of the present invention will be described withrespect to communication efficient sparse-reduce in distributed machinelearning. As readily appreciated by one of ordinary skill in the art,the preceding embodiments will likely have overlapping disclosureaspects given their underlying relation to each other.

The description relating to distributed machine learning may be soprovided relative to large scale surveillance for the sake ofillustration and concreteness. However, as readily appreciated by one ofordinary skill in the art, the present invention can be applied to amyriad of other distributed machine learning based applications, giventhe teachings of the present invention provided herein, whilemaintaining the spirit of the present invention.

The description will now commence relating to fine-grainedsynchronization for data-parallel tasks in a big data processingenvironment.

In an embodiment, in order to provide an efficient wait mechanism forpartial reduce operations, the present invention uses a notify mechanismwith respect to the sender when sending updated output values to thesender. With parallel threads over a shared memory or Remote DirectMemory Access (RDMA), a send operation may not notify the receiver aboutthe incoming parameters. In an embodiment of the present invention, aper-receiver notification allows for fine-grained synchronization andremoves the inefficiency that is introduced by a global barrier.

To reduce the barrier overhead for partial-reduce operations and forstrong consistency, the present invention provides a notify-ack(notify-acknowledgement) based mechanism that gives stricter guaranteesthan a single barrier and can improve performance in some cases. Allprocesses compute and send their model parameters and send notificationsto the receivers. The receiver consumes the model parameters andperforms a reduce operation and sends an acknowledgment to all itssenders indicating that it has consumed its gradient. Hence, when usinga notify-ack based service, each receiver acknowledges processing ofincoming model parameters to the receivers. This removes the problem ofmixed-version vectors. Furthermore, this fine-grained synchronizationallows efficient implementation of partial reduce operations since eachsender is only blocked on its incoming receivers.

Fine-grained synchronization in accordance with the present inventionachieves correctness and performance improvements over many big data,data parallel jobs. Such big data, data parallel jobs include, but arenot limited to, machine learning, graph processing, log processing, andso forth. Essentially, the present invention can be applied to anyparallel computing environment, as readily appreciated by one ofordinary skill in the art, given the teachings of the present inventionprovided herein. To the preceding and other applications, the presentinvention provides: (i) faster processing; (ii) correct execution andsynchronization semantics as compared to a barrier; and (iii) loadbalanced network sharing.

Referring now in detail to the figures in which like numerals representthe same or similar elements and initially to FIG. 1, a block diagramillustrating an exemplary processing system 100 to which the presentprinciples may be applied, according to an embodiment of the presentprinciples, is shown. The processing system 100 includes at least oneprocessor (CPU) 104 operatively coupled to other components via a systembus 102. A cache 106, a Read Only Memory (ROM) 108, a Random AccessMemory (RAM) 110, an input/output (I/O) adapter 120, a sound adapter130, a network adapter 140, a user interface adapter 150, and a displayadapter 160, are operatively coupled to the system bus 102. At least oneGraphics Processing Unit (GPU) 194 is operatively coupled to the CPU 104and/or other elements of system 100 via system bus 102.

A first storage device 122 and a second storage device 124 areoperatively coupled to system bus 102 by the I/O adapter 120. Thestorage devices 122 and 124 can be any of a disk storage device (e.g., amagnetic or optical disk storage device), a solid state magnetic device,and so forth. The storage devices 122 and 124 can be the same type ofstorage device or different types of storage devices.

A speaker 132 is operatively coupled to system bus 102 by the soundadapter 130. A transceiver 142 is operatively coupled to system bus 102by network adapter 140. A display device 162 is operatively coupled tosystem bus 102 by display adapter 160.

A first user input device 152, a second user input device 154, and athird user input device 156 are operatively coupled to system bus 102 byuser interface adapter 150. The user input devices 152, 154, and 156 canbe any of a keyboard, a mouse, a keypad, an image capture device, amotion sensing device, a microphone, a device incorporating thefunctionality of at least two of the preceding devices, and so forth. Ofcourse, other types of input devices can also be used, while maintainingthe spirit of the present principles. The user input devices 152, 154,and 156 can be the same type of user input device or different types ofuser input devices. The user input devices 152, 154, and 156 are used toinput and output information to and from system 100.

Of course, the processing system 100 may also include other elements(not shown), as readily contemplated by one of skill in the art, as wellas omit certain elements. For example, various other input devicesand/or output devices can be included in processing system 100,depending upon the particular implementation of the same, as readilyunderstood by one of ordinary skill in the art. For example, varioustypes of wireless and/or wired input and/or output devices can be used.Moreover, additional processors, controllers, memories, and so forth, invarious configurations can also be utilized as readily appreciated byone of ordinary skill in the art. These and other variations of theprocessing system 100 are readily contemplated by one of ordinary skillin the art given the teachings of the present principles providedherein.

Moreover, it is to be appreciated that environment 200 described belowwith respect to FIG. 2 is an environment for implementing respectiveembodiments of the present principles. Part or all of processing system100 may be implemented in one or more of the elements of environment200.

Further, it is to be appreciated that processing system 100 may performat least part of the method described herein including, for example, atleast part of method 500 of FIG. 5 and/or at least part of method 600 ofFIG. 6 and/or at least part of method 800 of FIG. 8 and/or at least partof method 900 of FIG. 9. Similarly, part or all of environment 200 maybe used to perform at least part of method 500 of FIG. 5 and/or at leastpart of method 600 of FIG. 6 and/or at least part of method 800 of FIG.8 and/or at least part of method 900 of FIG. 9.

FIG. 2 shows an exemplary environment 200 to which the present inventioncan be applied, in accordance with an embodiment of the presentprinciples.

The environment 200 includes a set of computing nodes (collectively andindividually denoted by the figure reference numeral 210). Each of thecomputing nodes in the set 210 is configured to perform data paralleljobs and to perform fine-grained synchronization for the data paralleljobs.

In an embodiment, each of the computing nodes 210 is a parallel worker.In an embodiment, none of the computing nodes 210 is a master node. Inanother embodiment, one of the computing nodes 210 is a master node.

The set of computing nodes 210 can be configured to implement MapReduceoperations, a Message Passing Interface (MPI), and so forth.

The set of computing nodes 210 can be implemented by, for example,separate computing devices (such as, e.g., in a distributed arrangement)or different items (threads, processes, etc.) in a single computingdevice. Of course, other implementations can also be employed, whilemaintaining the spirit of the present invention.

The set of computing nodes 210 are interconnected by a communicationmedium 280. The communication medium 280 can involve any type ofcommunication medium, depending upon the implementation. For example, abus, a network, a Message Passing Interface (MPI), and so forth can beused, while maintaining the spirit of the present invention.

FIG. 3 shows an exemplary synchronization condition 300 to which thepresent invention can be applied, in accordance with an embodiment ofthe present principles. The synchronization condition 300 involvesworkers W1-W5. The following synchronization semantics apply: (i)workers W1, W2 and W3 synchronize with one another; (ii) workers W3, W4and W5 synchronize with one another. The synchronization condition 300uses a barrier condition 366.

With the current synchronization methods in Hadoop®, Spark and othermachine learning and graph learning frameworks, all workers wait foreveryone at the barrier and then proceed to the next iteration.

FIG. 4 shows an exemplary synchronization condition 400, in accordancewith an embodiment of the present principles.

The synchronization condition 400 involves the same workers andsynchronization semantics as shown in FIG. 3, with the exception that nobarrier condition is used. That is, the synchronization condition 300does not use a barrier condition.

The solid lines represent a SEND (updates, e.g., but not limited to,model parameters) and a NOTIFY (notification) and the dotted linesrepresent a corresponding ACK (acknowledgement). The corresponding ACKcan be sent by respective ones of the workers, for example, after therespective ones of the workers perform a reduce process. Workers onlywait for their dependencies and continue with the next iteration as soonas they receive the NOTIFY from all incoming nodes.

FIG. 5 shows an exemplary method 500 for fine-grain synchronization ofdata parallel jobs, in accordance with an embodiment of the presentprinciples. In an embodiment, method 500 can be used for data paralleljobs for distributed machine learning.

At step 510, synchronize respective ones of a plurality of data parallelworkers with respect to an iterative process. In an embodiment, therespective ones of the plurality of data parallel workers can consist ofa subset of the plurality of data parallel works. In an embodiment, theiterative process can be an iterative distributed machine learningprocess.

In an embodiment, step 510 includes step 510A.

At step 510A, individually continue, by the respective ones of theplurality of data parallel workers, from a current iteration to asubsequent iteration of the iterative process (e.g., an iterativedistributed machine learning process), responsive to a satisfaction ofthe predetermined condition thereby.

In an embodiment, the predetermined condition of step 510A includessteps 510A1 and 510A2.

At step 510A1, individually send a per-receiver notification from eachsending one of the plurality of data parallel workers to each receivingone of the plurality of data parallel workers, responsive to a sendingof data there between.

At step 510A2, individually send a per-receiver acknowledgement from thereceiving one to the sending one, responsive to a consumption of thedata thereby.

The method 600 specifically relates to an example where the involvedparallel workers performing a reduce process. Of course, the presentinvention can be applied to other processes that can use and benefitfrom fine-grain synchronization in accordance with the presentinvention. In general, workers only wait for intermediate outputs fromdependent workers to perform the reduce process. After the reduceprocess, the workers push more data out when the workers receive an ACKfrom receivers signaling that the sent parameter update has beenconsumed.

At step 610, send updates (e.g., model parameters) and a notification(NOTIFY), from some data parallel workers to other ones (from a subsetup to all remaining ones) of the data parallel workers.

At step 620, wait for the notification (NOTIFY), by each respective dataparallel worker from all of its senders (i.e., from the data parallelworkers that sent that respective data parallel worker an update).Hence, there is some gap in time or some other segregation between whenthe update and the NOTIFY are received from a sender (sending dataparallel worker).

In an embodiment, step 620 includes step 620A.

At step 620A, count, for each of the data parallel workers) the numberof notifications (NOTIFYs) received by each of its senders.

At step 630, determine, for each respective data parallel worker,whether the count for that respective data parallel worker is equal tothe number of all of its senders. If so, then proceed to step 640.Otherwise, return to step 620.

At step 640, perform a reduce process. It is to be appreciated that step640 is only performed by a respective data parallel worker responsive tothe NOTIFY being received by that respective data parallel worker fromall of its senders.

At step 650, send an acknowledgement (ACK), by each of the respectivedata parallel workers responsive to that respective data parallel workerhaving performed the reduce process.

At step 660, send updates, from only the respective data parallelworkers that have sent an acknowledgement (ACK) at step 650.

A description will now be given regarding some of the many attendantfeatures of the present invention relating to at least the embodimentsdirected to fine-grain synchronization in data-parallel jobs. Onefeature is the use of fine-grained synchronization instead of a globalbarrier to synchronize between the workers of a data-parallel jobs. Thisimproves performance if a subset of workers wants to synchronize.Moreover, the present invention reduces torn-reads (reads ofincompletely written data) that may occur with barriers. Also, thepresent invention improves network bandwidth utilization since allworkers do not send and wait at the same time.

The description will now commence relating to fine-grainedsynchronization for data-parallel tasks for distributed machinelearning, in accordance with an embodiment of the present invention.

We modify the distributed training in parallel-learning systems forimproved coordination and synchronization.

In consideration of applying the present invention for fine-grainsynchronization in data parallel jobs for distributed machine learning,in an embodiment, at least some of computing nodes 210 in FIG. 2 can beconsidered to be located in disparate locations with respect to eachother in a distributed configuration, such that communication medium 280allows for communication between these nodes 210 and can involve variousdifferent types and/or configurations of communication mediums, asreadily appreciated by one of ordinary skill in the art, given theteachings of the present invention provided herein. That is, thecommunication types and/or configurations involved can vary fromembodiment to embodiment, depending upon the specific application, whilemaintaining the spirit of the present invention.

Exemplary applications to which embodiments directed fine-grainsynchronization in data parallel jobs for distributed machine learningcan, in turn, be directed to, include, but are not limited to,large-scale surveillance, language translation, and image recognition.The surveillance can be, for example, over a node(s) of GPUs and/orCPUs. Other surveillance targets can also be used, while maintaining thespirit of the present invention. It is to be appreciated that thepreceding applications are merely illustrative and, thus, one ofordinary skill in the art given the teachings of the present inventionprovided herein, would contemplate these and a myriad of otherapplications to which the present invention can be applied, whilemaintaining the spirit of the present invention.

A description will now be given regarding some of the many attendantfeatures of the present invention relating to at least the embodimentsdirected to fine-grain synchronization in data-parallel jobs fordistributed machine learning. One feature is faster model training ofcomputing the machine learning models. Other features include correctexecution and synchronization semantics as compared to a barrier togenerate the models. Still another feature is load balanced networksharing during distributed model training.

The description will now commence relating to communication efficientsparse-reduce in distributed machine learning.

To that end, an embodiment of the present invention provides a novelreduce operation during distributed training of the models such as, forexample, surveillance models. Of course, other types of models can alsobe used including, but noted limited to, language translation models,and image recognition models.

We modify the distributed training in parallel-learning systems forreduced latency during “reduce operation” with the same convergencerates.

We propose a spectral-reduce where we decide on a fixed communicationcost and decide on communication architecture such that the overallresulting communication graph has a high spectral gap.

We start with a communication graph that includes all machines in agiven cluster. We start with a fixed communication cost, which can beempirically determined and allows us to pick the out-degree of each nodein the graph. A goal is how to determine a sparse graph such that thegraph has good information dispersal properties with this fixedcommunication cost. By the term “good information dispersal properties”,we mean that the nodes are connected in such a manner that theintermediate output from one node (i.e., parameter updates in the caseof parallel machine learning) is dispersed to all other nodes in thefewest (possible) time steps. If the nodes are connected in a chain-likefashion, then the intermediate outputs from node i may spread to i+1 ina single time step but will take N time steps to reach to the last nodein the cluster. Hence, intuitively well-connected graphs converge fasterbut have high communication costs.

In order to measure how every node diffuses its intermediate results(model parameters), we take the adjacency matrix and divide with by thein-degree of each node in the communication graph to obtain a quotient“P”. We compress this representation to a vector by computing the secondlargest singular value of P, and calculate the spectral gap as follows:

1−σ2(P),

where σ2(P) is the second largest singular value of P (which denotes thetransition matrix). The transition matrix P is defined as A/d, where Ais the adjacency matrix (including self-loop) and d is the in-degree(including self-loop). The spectral gap here is defined as σ1(P)−σ2(P).However, σ1(P), which denotes the largest singular value, should be 1.Hence, the gap equals 1−σ2(P). The high spectral gap ensures that modelupdates from one node are propagated over the network rapidly ensuringfast convergence. We call this sparse reduce step where the underlyingcommunication node graph has a high spectral gap as “spectral-reduce”.

FIG. 7 shows a comparison involving an all-reduce 710 and a parameterserver 720 to which the present invention can be applied, and a spectralreduce 730 in accordance with an embodiment of the present invention.

In FIG. 7, a circle having a “W” followed by an integer represents arespective worker (machine), and a circle having a “M” followed by aninteger represents a respective machine-learning model. Amachine-learning model can include data and model parameters. Thesemachines train machine-learning models on this data iteratively. Everyiteration produces a model update. These updates need to be propagatedto all other machines that are training in parallel with data from thesame dataset. In FIG. 7, the models are shown communicating with allmachines to send model updates. All-reduce exchange of model updates.All of the depicted arrows indicate bi-directional communication. Asnumber of nodes (N) grows, the total number of updates transmittedincreases to O(N̂2).

In particular, all-reduce 710 and parameter server 720 involve existingcommunication architectures to which the present invention can beapplied, in accordance with an embodiment of the present invention. Incontrast, the present invention advantageously provides spectral reduce730, which connects different machines based on an underlying graph withhigh spectral gap. Instead of all machines sending updates to everyother machine, spectral reduce 730 models communication in a sparsefashion such that the underlying node communication graph has a highspectral gap value. This reduces network communication which results inspeeding up model training time.

FIG. 8 shows a method 800 for communication efficient sparse-reduce in adistributed machine learning environment, in accordance with anembodiment of the present invention. The method 800 can be used, forexample, to reduce the model training time in the parallel processing ofmachine learning models as applied to various applications including,but not limited to, surveillance, language translation, and imagerecognition. The method 800 advantageously speeds up the model trainingtime in a parallel machine learning environment by reducing networkcommunication in the parallel machine learning environment. The networkcommunication is reduced by limiting model update propagation in theparallel machine learning environment using a sparse communicationmodel. In an embodiment, the parallel machine learning environment canbe a distributed parallel machine learning environment. In anembodiment, method 800 is applied to an iterative distributed machinelearning process for distributive training of a set of surveillancemodels. The set of surveillance models can be trained, for example, toperform a set of surveillance tasks responsive to certain stimuli.

At block 810, input a communication graph that includes all the machinesin a target cluster (e.g., to be surveilled and/or otherwiseprocessed/analyzed/etc.) of the parallel machine learning environment.In an embodiment, each machine can be a stand-alone machine (e.g., aserver, and so forth) or can be a computing device(s) in a stand-alonemachine (e.g., a central processing unit, a graphical processing unit,and so forth). In an embodiment, the communication graph can depictindividual machines as nodes and connections of the nodes as edges. Ofcourse, other topology configurations can be used. In an embodiment, theparallel machine learning environment may only include the targetcluster (having multiple machines therein for parallel computing). Inanother embodiment, the parallel machine learning environment mayinclude multiple clusters, each having multiple machines therein forparallel computing, and each processed in accordance with method 200 toensure optimal communication in each of the multiple clusters.

At block 820, determine a fixed communication cost for a sparse graph tobe computed. The sparse graph is (i) determined from the communicationgraph, and (ii) represents a communication network (for the cluster)having (a) a high overall spectral gap, and (b) certain informationdispersal properties. The high overall spectral gap and the certaininformation dispersal properties are further described herein withrespect to at least block 830. In an embodiment, the fixed communicationcost can be determined empirically. In an embodiment, the fixedcommunication cost can be determined to allow selection of theout-degree for each node in the sparse graph.

At block 830, compute the sparse graph, based on the communication graphand the fixed communication cost.

The high overall spectral gap of the sparse graph ensures that modelupdates from one node of the cluster are propagated over the (cluster)network to other nodes of the cluster rapidly, ensuring fastconvergence. As used herein, the term “high overall spectral gap” refersto a value as close to 1 as possible (noting that the spectral gapvaries from 0.0 to 1.0). In an embodiment, the high overall spectral gapcan be approximated as the second eigenvalue of a brute force search of[low connectivity] circulant graphs and a concrete threshold can bedefined as 2.0 times that value. However, in general “as close to 1 aspossible” is the preferred high overall spectral gap employed by thepresent invention. In an embodiment, the overall spectral gap can bedetermined relative to a minimum overall spectral gap threshold (asdescribed above) such that if the computed overall spectral gap is equalto or greater than the threshold, then the overall spectral gap isconsidered “high”.

As used herein, the term “certain information dispersal properties” canrefer to the sparse graph having node connections such that anintermediate output (model update) from a given node disperses to allother nodes of the sparse graph in the fewest time steps (given otherpossible node connections resulting in different (i.e., more) timesteps).

In an embodiment, block 830 includes block 830A.

At block 830A, automatically select the number and type of replicas forthe spectral reduce (that is, for computing the sparse graph) based onthe spectral gap of the network and the number of edges in thecommunication graph. As used herein, the term “replica”, alsointerchangeably referred to as “model replica” herein, refers to a modelor a model portion that is replicated for the purpose of training themodel or the model portion using data-parallel distributed machinelearning. For example, the spectral gap of the network and the number ofedges can be used as input functions for an optimizer or learningfunction configured to make the automatic selection of block 830. Theoptimizer or learning function can be implemented, for example, bysoftware stored in memory 110 and executed by CPU 104 and/or GPU 194.

At block 840, propagate model updates in the parallel machine learningenvironment based on (e.g., using a topology of) the sparse graph. Inthis way, the limited communication resulting from use of the sparsegraph will limit the overall intra-cluster communication (of modelupdates), thus speeding up model training.

FIG. 9 shows a method 900 for measuring node diffusion efficiency, inaccordance with an embodiment of the present invention.

At block 910, divide an adjacency matrix of the (node) cluster by anin-degree of each node in the communication graph to obtain a quotientP.

At block 920, compress the quotient P to a vector by computing a secondlargest singular value of P, and calculating the spectral gap as1−σ2(P), where σ2(P) is the second largest singular value of P. The highspectral gap ensures that model updates from one node are propagatedover the network rapidly ensuring fast convergence. This sparse reducestep where the underlying communication node graph has a high spectralgap as “spectral-reduce”.

A description will now be given regarding some of the many attendantfeatures of the present invention relating to at least the embodimentsdirected to communication efficient sparse-reduce in distributed machinelearning. One feature is that by using a network-efficient parallelmodel, the resultant training results in faster model training times forall distributed machine learning applications. This happens because ofat least the following: (1) the amount of data transmitted is reduced;and (2) in a synchronized implementation, this reduces the number ofincoming updates that each node needs to wait before going on to thenext iteration. Furthermore, our solution reduces the need for highbandwidth interfaces, reducing costs or freeing up the network for otherapplications.

This is beneficial because this reduces the turn-around time inretraining the models. For example, for surveillance applications, onemay be interested in capturing new events and models periodically. Withthe present invention, this can be accomplished quickly, reducing theoverall time required to update the models with the latest data.

Embodiments described herein may be entirely hardware, entirely softwareor including both hardware and software elements. In a preferredembodiment, the present invention is implemented in software, whichincludes but is not limited to firmware, resident software, microcode,etc.

Embodiments may include a computer program product accessible from acomputer-usable or computer-readable medium providing program code foruse by or in connection with a computer or any instruction executionsystem. A computer-usable or computer readable medium may include anyapparatus that stores, communicates, propagates, or transports theprogram for use by or in connection with the instruction executionsystem, apparatus, or device. The medium can be magnetic, optical,electronic, electromagnetic, infrared, or semiconductor system (orapparatus or device) or a propagation medium. The medium may include acomputer-readable medium such as a semiconductor or solid state memory,magnetic tape, a removable computer diskette, a random access memory(RAM), a read-only memory (ROM), a rigid magnetic disk and an opticaldisk, etc.

It is to be appreciated that the use of any of the following “/”,“and/or”, and “at least one of”, for example, in the cases of “A/B”, “Aand/or B” and “at least one of A and B”, is intended to encompass theselection of the first listed option (A) only, or the selection of thesecond listed option (B) only, or the selection of both options (A andB). As a further example, in the cases of “A, B, and/or C” and “at leastone of A, B, and C”, such phrasing is intended to encompass theselection of the first listed option (A) only, or the selection of thesecond listed option (B) only, or the selection of the third listedoption (C) only, or the selection of the first and the second listedoptions (A and B) only, or the selection of the first and third listedoptions (A and C) only, or the selection of the second and third listedoptions (B and C) only, or the selection of all three options (A and Band C). This may be extended, as readily apparent by one of ordinaryskill in this and related arts, for as many items listed.

Having described preferred embodiments of a system and method (which areintended to be illustrative and not limiting), it is noted thatmodifications and variations can be made by persons skilled in the artin light of the above teachings. It is therefore to be understood thatchanges may be made in the particular embodiments disclosed which arewithin the scope and spirit of the invention as outlined by the appendedclaims. Having thus described aspects of the invention, with the detailsand particularity required by the patent laws, what is claimed anddesired protected by Letters Patent is set forth in the appended claims.

What is claimed is:
 1. A computer-implemented method for sparsecommunication in a parallel machine learning environment, comprising:determining, by a processor, a fixed communication cost for a sparsegraph to be computed, wherein the sparse graph is (i) determined from acommunication graph that includes all the machines in a target clusterof the parallel machine learning environment, and (ii) represents acommunication network for the target cluster having (a) an overallspectral gap greater than or equal to a minimum threshold, and (b)certain information dispersal properties such that an intermediateoutput from a given node disperses to all other nodes of the sparsegraph in lowest number of time steps given other possible nodeconnections; computing, by the processor, the sparse graph, based on thecommunication graph and the fixed communication cost; and initiating, bythe processor, a propagation of the intermediate output in the parallelmachine learning environment using a topology of the sparse graph. 2.The computer-implemented method of claim 1, further comprisingautomatically selecting a number and a type of model replicas forcomputing the sparse graph, based on the overall spectral gap and anumber of edges in the communication graph.
 3. The computer-implementedmethod of claim 1, wherein the fixed communication cost is determinedempirically.
 4. The computer-implemented method of claim 1, wherein thefixed communication cost is determined to allow selection of anout-degree for each node in the sparse graph.
 5. Thecomputer-implemented method of claim 1, wherein the intermediate outputis a model update for model training.
 6. The computer-implemented methodof claim 1, wherein the parallel machine learning environment is adistributed parallel machine learning environment.
 7. Thecomputer-implemented method of claim 1, wherein the parallel machinelearning environment is comprised in a surveillance system.
 8. Thecomputer-implemented method of claim 1, wherein the parallel machinelearning environment is comprised in a language translation system. 9.The computer-implemented method of claim 1, wherein the parallel machinelearning environment is comprised in an image recognition system. 10.The computer-implemented method of claim 1, wherein the method isperformed to train a parallel model in a distributed manner usingmultiple computing nodes of the target cluster.
 11. A computer programproduct for sparse communication in a parallel machine learningenvironment, the computer program product comprising a non-transitorycomputer readable storage medium having program instructions embodiedtherewith, the program instructions executable by a computer to causethe computer to perform a method comprising: determining, by a processorof the computer, a fixed communication cost for a sparse graph to becomputed, wherein the sparse graph is (i) determined from acommunication graph that includes all the machines in a target clusterof the parallel machine learning environment, and (ii) represents acommunication network for the target cluster having (a) an overallspectral gap greater than or equal to a minimum threshold, and (b)certain information dispersal properties such that an intermediateoutput from a given node disperses to all other nodes of the sparsegraph in lowest number of time steps given other possible nodeconnections; computing, by the processor, the sparse graph, based on thecommunication graph and the fixed communication cost; and initiating, bythe processor, a propagation of the intermediate output in the parallelmachine learning environment using a topology of the sparse graph. 12.The computer program product of claim 11, wherein the method furthercomprises automatically selecting a number and a type of model replicasfor computing the sparse graph, based on the overall spectral gap and anumber of edges in the communication graph.
 13. The computer programproduct of claim 11, wherein the fixed communication cost is determinedempirically.
 14. The computer program product of claim 11, wherein thefixed communication cost is determined to allow selection of anout-degree for each node in the sparse graph.
 15. The computer programproduct of claim 11, wherein the intermediate output is a model updatefor model training.
 16. The computer program product of claim 11,wherein the parallel machine learning environment is a distributedparallel machine learning environment.
 17. The computer program productof claim 11, wherein the parallel machine learning environment iscomprised in a surveillance system.
 18. The computer program product ofclaim 11, wherein the parallel machine learning environment is comprisedin a language translation system.
 19. The computer program product ofclaim 11, wherein the parallel machine learning environment is comprisedin an image recognition system.
 20. A computer processing system forsparse communication in a parallel machine learning environment,comprising: a memory for storing program code; and a processor forrunning the program code to: determine a fixed communication cost for asparse graph to be computed, wherein the sparse graph is (i) determinedfrom a communication graph that includes all the machines in a targetcluster of the parallel machine learning environment, and (ii)represents a communication network for the target cluster having (a) anoverall spectral gap greater than or equal to a minimum threshold, and(b) certain information dispersal properties such that an intermediateoutput from a given node disperses to all other nodes of the sparsegraph in lowest number of time steps given other possible nodeconnections; compute the sparse graph, based on the communication graphand the fixed communication cost; and initiate a propagation of theintermediate output in the parallel machine learning environment using atopology of the sparse graph.